One-dimensional spherical ray-tracing extended to account for flat and cylindrical shields

It is often desirable to compute the uncollided component (direct from the source) of a detected particle flux using some form of ray-tracing, which in one-dimensional spherical geometries is extremely economical. A simple method for treating a flat shield exactly, within the context of spherical ray-tracing, is presented. A method for treating a cylindrical shield approximately, using the average value of the azimuthal angle for each value of the polar angle that is used in the spherical ray-tracing, is presented. The source remains spherical. The methods are verified numerically with a test problem that also shows the importance of these corrections.